Local Scale-Invariance in Disordered Systems

Abstract

Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can describe data for either non-glassy systems quenched to below Tc or else for spin glasses at criticality. The dependence of the scaling behaviour on the distribution of the random couplings is discussed. It is shown that finite-time corrections to scaling can become quite sizable in these systems. Numerically determined ageing quantities are confronted with available experimental results.

Aging logarithmic conformal field theory: a holographic view

“…The two-time correlation function of the geometric realizations with aging isometry is identified and analyzed in the aging regime [11], reproducing the characteristic features of its time dependence: slow power-law decay, broken time translation invariance and dynamical scaling [12]. Here we would like to analyze the full profile of the correlation function without the logarithmic extensions, motivated by the recent interest in the field theory side [8] [9].…”

“…The correlation functions show the typical behaviors: older systems with a bigger waiting time relax in a slower manner than younger systems with smaller waiting time, see e.g. [2][5] [12] for reviews.…”

“…The resulting two-time correlation functions show a dissipative behavior and exhibit the characteristic features of the aging system: power law decay, broken time translation invariance and dynamical scaling between the time and spatial directions [11], see also e.g. [2][5] [12] from the field theory point of view. These properties are shown in the geometric realizations of the aging background in the context of [14] [15] as well as of the aging in light-cone in the context of [17] [18].…”

Aging and holography

“…One of the simplest notions of nonequilibrium physics is aging, which corresponds to 'non-equilibrium criticality,' in a sense that we will make more precise below. If a physical system is brought rapidly out of equilibrium by a sudden change of an external control parameter (quenching), one often finds (i) slow (non-exponential) dynamics, (ii) breaking of time translation invariance and (iii) dynamical scaling [1], [2]. We will show that aging phenomena [3] can be studied by deforming a variant of gauge/gravity duality [4,5] with isometries given by the Schrödinger algebra.…”

“…A crucial step in the theoretical description of some far from equilibrium phenomena was the realization of the role of local scale invariance [2,11,12,13]. In the particular case of aging phenomena [14], where it is observed that the properties of non-equilibrium systems generically depend on time since the system was brought out of equilibrium, the role of a sub-algebra of the Schrödinger algebra with dynamical exponent z = 2 has been found to be crucial [15,16].…”